How should monetary policy respond to a global liquidity trap, where the two countries may fall into a liquidity trap simultaneously? Using a two-country New Open Economy Macroeconomics model, we first characterise optimal monetary policy, and show that the optimal rate of inflation in one country is affected by whether or not the other country is in a liquidity trap. We next examine how well the optimal monetary policy is approximated by relatively simple monetary policy rules. The interest-rate rule targeting the producer price index performs very well in this respect.